Algebra Basics - 2

Algebra Level 2

a = b a=b Step 1: Multiply both sides by a a a 2 = a b a^2 = ab Step 2: Subtract both sides by b 2 b^2 a 2 − b 2 = a b − b 2 a^2 - b^2 = ab - b^2 Step 3: Factorize. ( a − b ) ( a + b ) = b ( a − b ) (a-b)(a+b) = b(a-b) Step 4 : Cancel ( a − b ) (a-b) from both sides. a + b = b a+b = b Step 5:Subtract b b from both sides a = 0 a=0 ∴ a n y n u m b e r = 0 \therefore any \ number = 0

This is an incorrect proof. Which was the first step when a mistake occurred?

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Mohammad Farhat by Mohammad Farhat , 16, Singapore

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2 solutions

Mohammad Farhat
Jun 3, 2019

Remember the proof started with a = b a=b so what does a − b a-b equal?

0. \large 0.

So what does it mean to divide by 0?

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Lâm Lê
Sep 4, 2020

Y o u c a n n o t d i v i d e b y 0 \Huge You \ can \ not \ divide \ by \ 0

S t e p 4 c o n t a i n s d i v i d i n g b y 0 ⇒ S t e p 4 i s w r o n g Step \ 4 \ contains \ dividing \ by \ 0\Rightarrow \boxed{Step \ 4 \ is \ \color{#D61F06}wrong}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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